In recent years, a type of cooling device has been put into practical use that uses a pump, such as an electric water pump, which is capable of varying the discharge amount independently of the operating state of an engine. In an internal combustion engine equipped with such a pump, the discharge amount of the pump is limited when the coolant temperature is relatively low, for example, during a warm-up to suppress the heat exchange between the whole engine and coolant, thereby promoting the warm-up (for example, refer to Patent Document 1).